10 identical bottles of pills

We have 10 identical bottles of identical pills (each bottle contain hundred of pills). Out of 10 bottles 9 have 1 gram of pills but 1 bottle has pills of weight of 1.1 gram. Given a measurement scale, how would you find the heavy bottle? You can use the scale only once.

Answer:

First, arrange the bottles on shelf and now take, 1 pill from the first bottle, 2 pills from the second bottle, 3 pills from the third bottle, and so on. Ideally you would have (10)*(11)/2=55 pills weighing 55 grams, when you put the entire pile of pills on the weighing scale.The deviation from 55 g would tell you which bottle contains the heavy pills.

If it is .1 gram more, it is 1st bottle which has heavy pill, if it is .2 more, gram 2nd bottle has heavy pills, if it is .3 more, gram 3rd bottle has heavy pills.

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Divide 10 bottles into group of 2 (5 bottle each) Now wight them now take out the group which is more in wight. Repeat the process until you found the heavier bottle. It will take less number of comparision.

Divide 10 bottles into group of 2 (5 bottle each) Now wight them now take out the group which is more in wight. Repeat the process until you found the heavier bottle. It will take less number of comparison.